Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917002932649984 |
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| author | Coudreuse, Fanch |
| author_facet | Coudreuse, Fanch |
| contents | We establish a version of the Li--Yau--Hamilton inequality for the Granular-Medium equation on the torus, both at the PDE level and for its time-discrete approximation given by the JKO scheme. We then apply this estimate to derive further quantitative results for the continuous and discrete JKO flows, including Lipschitz and $L^\infty$ bounds, as well as a quantitative Harnack inequality. Finally, we use the regularity provided by this estimate to show that the JKO scheme for the Fokker--Planck equation converges in $L^2_{\mathrm{loc}}((0,+\infty); H^2(\mathbb{T}^d))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation Coudreuse, Fanch Analysis of PDEs Optimization and Control We establish a version of the Li--Yau--Hamilton inequality for the Granular-Medium equation on the torus, both at the PDE level and for its time-discrete approximation given by the JKO scheme. We then apply this estimate to derive further quantitative results for the continuous and discrete JKO flows, including Lipschitz and $L^\infty$ bounds, as well as a quantitative Harnack inequality. Finally, we use the regularity provided by this estimate to show that the JKO scheme for the Fokker--Planck equation converges in $L^2_{\mathrm{loc}}((0,+\infty); H^2(\mathbb{T}^d))$. |
| title | Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2510.09231 |